Ecosystems (2010) 13: 841–850
DOI: 10.1007/s10021-010-9358-x
Ó 2010 The Author(s). This article is published with open access at Springerlink.com
Alternative Stable States Driven
by Density-Dependent Toxicity
Tjisse van der Heide,1,2* Egbert H. van Nes,3 Marieke M. van Katwijk,1
Marten Scheffer,3 A. Jan Hendriks,1 and Alfons J. P. Smolders2
1
Department of Environmental Science, Institute for Wetland and Water Research, Faculty of Science, Radboud University Nijmegen,
P.O. Box 9010, 6500 GL Nijmegen, The Netherlands; 2Department of Environmental Biology, Institute for Water and Wetland
Research, Faculty of Science, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands; 3Aquatic Ecology
and Water Quality Management Group, Department of Environmental Sciences, Wageningen University, P.O. Box 8080, 6700 DD
Wageningen, The Netherlands
ABSTRACT
we demonstrated that ammonia toxicity in eelgrass
is highly dependent on the eelgrass shoot density.
Here, we used the results of these experiments to
construct a model describing the complex interactions between the temperate seagrass Zostera marina
and potentially lethal ammonia. Analyses of the
model show that alternative stable states are indeed
present over wide ranges of key-parameter settings,
suggesting that the mechanism might be important
especially in sheltered, eutrophicated estuaries
where mixing of the water layer is poor. We argue
that the same mechanism could cause alternative
stable states in other biological systems as well.
Many populations are exposed to naturally occurring or synthetic toxicants. An increasing number
of studies demonstrate that the toxicity of such
compounds is not only dependent on the concentration or load, but also on the biomass or density
of exposed organisms. At high biomass, organisms
may be able to alleviate adverse effects of the toxicant by actively lowering ambient concentrations
through either a joint detoxification mechanism or
growth dilution. We show in a conceptual model
that this mechanism may potentially lead to alternative stable states if the toxicant is lethal at low
densities of organisms, whereas a high density is
able to reduce the toxicant concentrations to sublethal levels. We show in an example that this effect may be relevant in real ecosystems. In an
earlier published experimental laboratory study,
Key words: alternative stable states; bistability;
density-dependence; toxicity; ammonia; ammonium; seagrass; Zostera marina.
INTRODUCTION
In their environments, organisms can be exposed to
a wide range of naturally occurring or synthetic
toxic substances (Moriarty 1999). Physiological or
population effects of such chemicals are mostly
examined in dose–response studies, where the
dosage of a toxicant is varied on a certain biomass
of organisms (Moriarty 1999). However, an
increasing number of studies demonstrate that
toxicity effects may often not only be dependent on
the dose, but also on the biomass of exposed
organisms. In such cases, toxicity may be alleviated
Received 31 October 2009; accepted 4 June 2010;
published online 16 July 2010
Electronic supplementary material: The online version of this article
(doi:10.1007/s10021-010-9358-x) contains supplementary material,
which is available to authorized users.
Author Contributions: Tjisse van der Heide and Egbert van Nes conceived of or designed study, performed research, analyzed data, contributed new methods or models, and wrote the article. Marieke van Katwijk
conceived of or designed study and wrote the article. Marten Scheffer and
Jan Hendriks wrote the article. Fons Smolders conceived of or designed
study, contributed new methods or models, and wrote the article.
*Corresponding author; e-mail: [email protected]
841
842
T. van der Heide and others
by a high organism biomass because the concentration of a toxicant is reduced to sub-lethal levels
due to joint uptake or active detoxification. This
effect has been described for a wide range of biological systems such as heavy metal accumulation
in organisms (Duxbury and McIntyre 1989; Pickhardt and others 2002), phytotoxins in microbes
and plants (for example, Weidenhamer and others
1989; Greig and Travisano 2008; Pollock and others
2008), and for drug treatments of infectious bacteria or cancer (for example, Brook 1989; Kobayashi and others 1992; Brandt and others 2004). In
ecotoxicological studies, this mechanism is often
referred to as ‘‘density-dependent toxicity’’ (for
example, Duxbury and McIntyre 1989; Kobayashi
and others 1992; van der Heide and others 2008) or
the ‘‘dilution effect’’ (for example, Karimi and
others 2007; Pollock and others 2008), whereas it is
described as the ‘‘inoculum effect’’ in many pharmaceutical studies (for example, Brook 1989;
Kobayashi and others 1992; Brandt and others 2004).
This density-dependent toxicity implies a positive
feedback between population density and toxic
substance concentration, because an increase in
biomass alleviates toxicity, which can in turn further amplify biomass growth. Theory suggests that
if such a positive feedback mechanism is strong
enough, it could lead to alternative stable states
(also called bistability) and hysteresis (Carpenter
2001; Scheffer and others 2001; Scheffer and Carpenter 2003). This implies that environmental
changes or disturbances (for example, disease) may
push the population beyond a critical threshold,
causing a collapse (for example, mass mortality) to
an alternative stable state (Scheffer and others
2001). Implications of non-linear response and
threshold behavior in biological systems can be
profound. Shifts in populations with positive feedbacks are typically hard to predict and recovery of a
collapsed system is often difficult.
In this study, we examine whether a positive
feedback caused by density-dependent toxicity may
cause alternative stable states. First, we show the
basic idea in a simple conceptual model, describing
a generalized positive feedback system between a
population of organisms and a toxic compound. We
analyzed two different assumptions of how an
established population can alleviate toxicity: the
organisms can alleviate toxicity actively (‘‘joint
detoxification’’) or can take up and store a limited
amount of the toxic substance per organism or unit
of biomass (‘‘growth dilution’’). Next, we created a
more realistic model, describing ammonia toxicity
in seagrass ecosystems, to further explore our theory for an empirical situation. We analyze whether
this model can have alternative stable states using
realistic parameter settings based on laboratory
experiments and literature.
METHODS
Conceptual Models
The basic mechanism of this feedback can be
shown in a very simple model. This model describes
a system with a population of organisms that cannot exceed a carrying capacity, for instance due to
limited nutrients, food or space. Furthermore, we
model a toxicant that increases mortality of the
population:
dX
X
¼a 1
X bX T
ð1Þ
dt
KX
X describes the biomass of the population, a is the
maximum net growth rate per unit of time and KX
is the carrying capacity. Parameter b is a mortality
constant which, multiplied with the concentration
of toxicant T represents the mortality rate in
population X per unit of time. Although the linear
effect of T in the model may often be an oversimplification of reality, simulations comparing linear,
Monod and Hill functions, showed that basic model
behavior is not sensitive to the choice of the
function here in the sense that it consistently produced alternative stable states in a wide parameter
range. Moreover, in many cases the response of
organisms to toxicants can well be described by this
simple relation (Hendriks and others 2005). The
second equation describes the change in toxic
compounds in the system per unit of time.
We assume a constant external input or internal
release of the toxicants similar to a chemostat
model (for example, Edelstein-Keshet 1988).
However, organisms can also reduce the concentration of toxicants in the system:
dT
¼ ðTin TÞ p T f ðXÞ
dt
ð2Þ
where Tin is the maximum equilibrium concentration of toxicants that can accumulate in the system
and p is the dilution rate (that is, the fraction of the
volume replaced per time unit). We assume that
the organisms reduce the concentration of toxicants as a function of their biomass. This densitydependent alleviation of toxicity is essential for the
feedback.
We analyzed two different assumptions. In the
first case, organisms can actively transform the toxic
compound into a harmless (or even useful) substance, for instance metabolically or by excretion of
Bistability Through Density-Dependent Toxicity
compounds that chemically react with the toxicant.
This mechanism can result in decreased mortality if
the density of organisms if sufficient to reduce
ambient toxicant concentrations (‘‘joint detoxification’’). Here, f(X) is described by d1 X, where d1 is a
constant describing the uptake rate of T per unit of
X. For the second mechanism, we assume that the
toxicant is not converted into a harmless substance,
but is stored is the tissues of the organisms (for
example, heavy metal storage in fat tissue). In this
case, organisms can only take up a limited amount of
the toxic substance per unit of biomass and detoxification is thus dependent on growth (‘‘growth
dilution’’). In this case, f(X) is replaced with the term
d2 a X (1 - X/Kx), where d2 describes the uptake of
T proportional to growth of X. Notably, net uptake of
the toxicant in the growth dilution model becomes
zero when carrying capacity is reached. In reality,
natural mortality and regrowth around carrying
capacity in the population would result in some
uptake and release dynamics of the toxicant. For
simplicity, however, we chose not to include a
mortality term in the models, because the general
behavior of the model would remain unchanged.
In systems with a relatively high dilution rate p,
dynamics of T are much faster than those of the
organisms. Therefore, we can assume a quasi
steady state (that is, dT ¼ 0) without any consedt
quences for the equilibrium density of organisms
and the behavior of the model. This assumption
simplifies the model to:
dX
X
pTin
¼a 1
ð3Þ
X bX
dt
KX
p þ f ðXÞ
The conditions for alternative stable states of this
simple model can be determined analytically for
the joint detoxification assumption or numerically
in case of the growth dilution model (online
Appendix 1).
Specific Model of NHx Toxicity
in Eelgrass
Recent studies have demonstrated that positive
feedbacks are important mechanisms in seagrass
ecosystems (van der Heide and others 2007, 2008,
2009). This model, based on empirical data, describes a feedback mechanism between the temperate seagrass Zostera marina (commonly called
eelgrass), reduced nitrogen (NHx) and potentially
lethal gaseous ammonia (NH3) in the water layer.
We chose this system as a more realistic analysis for
our theory because recent research demonstrated
that susceptibility of eelgrass to NHx toxicity is
843
highly dependent on vegetation density, indicating
that positive feedbacks between eelgrass and reduced nitrogen may lead to alternative stable states
in sheltered estuaries with high exposure to NHx. In
these systems, high concentrations of NHx may be
caused by for instance discharges of waste or river
water and degradation of phytoplankton or macroalgal mats (van der Heide and others 2008). Also,
because ammonium uptake is well studied in eelgrass, model parameters could be reliably estimated
based on these studies and results from our own
experimental work.
We based the model on the joint detoxification
assumption. In the first place because ammonium
is used as a nutrient by the plants and it is therefore
metabolized. Secondly, an eelgrass shoot may discard excess nutrients by replacing its leaves without
resorbing the nutrients stored in the leaves that
are lost (Hemminga and others 1999). Moreover,
compared to other vascular plants the lifespan of
eelgrass leaves is relatively short, suggesting that
excess nitrogen stored in the leaves may be
exported from the system through rejection of
leaves (Hemminga and others 1999).
In the model, survival of eelgrass is dependent on
the concentration of NH3 in the water layer. The
equation describing the change in eelgrass shoot
density per day (dZ/dt) is similar to Eq. 1:
dZ
Z
¼r 1
ð4Þ
Z m f ðNH3 Þ Z
dt
KZ
With r as the maximum net growth rate (day-1), KZ
as the carrying capacity (shoots m-2), and m as the
maximum mortality rate (day-1). The toxic effect
of NH3 is described by the function f(NH3). To
estimate the toxicity effect of NH3 in eelgrass, we
recalculated and analyzed experimental data of
Van der Heide and others (2008) (online Appendix
2). Our analyses revealed that toxicity by NH3 in
eelgrasses is best described by a Hill-curve (Figure 1). This is an equation that is typically used to
describe toxicity in organisms. The function expresses a sigmoid toxicity effect in the organism in
response to increasing exposure to a toxicant (Hill
1910):
M ¼ i þ Mmax
NHn3
þ HnNH3
NHn3
ð5Þ
Here M describes the fraction of leaf tissue mortality
in eelgrass after 5 days of exposure to NH3, i is the
background leaf mortality at zero exposure. HNH3 is
the half-saturation constant (mmol m-3) and n is a
dimensionless exponent determining the slope of
the curve. To describe the effect of NH3 in our
844
T. van der Heide and others
Bifurcation Analysis
Figure 1. Response of eelgrass shoots to ammonia at
varying concentrations after 5 days of exposure.
model, we adopted the part of Eq. 5 describing the
relative effect of NH3 on eelgrass mortality:
NHn3
f ðNH3 Þ ¼
NHn3 þ HnNH3
ð6Þ
In water, the total NHx concentration is made of the
sum of NH3 and ammonium (NH4+). NH3 and NH4+
are in equilibrium and the balance between these
compounds is determined by the pH of the water.
The concentration of NH3 in the water can be calculated from the pH and the total concentration of
reduced nitrogen in the water layer:
NH3 ¼
ka NHx
ka þ 10pH
ð7Þ
where ka is the dimensionless dissociation constant
of NHx in water with a salinity of 16 PSU at 20°C.
The change of NHx in the water layer is described
by the second differential equation:
dNHx
NHx
¼ ðNHx in NHx Þ R Umax
f ðZ Þ
dt
NHx þ HNHx
ð8Þ
With NHxin as the NHx concentration of the water
flowing into the meadow and R as the dilution rate
of the water inside the meadow. Umax is the maximum uptake rate of NHx by eelgrass (mmol g dry
weight-1 day-1) and HNHx is the half-saturation
constant for NHx uptake (mmol m-3). Finally,
f(Z) is a function describing the conversion from
eelgrass shoot density (shoot m-2) to the amount of
dry weight biomass per unit of volume:
f ðZ Þ ¼
Z
DwZ
C
ð9Þ
Here C is the height of the canopy (m) and DwZ is
the dry weight of one eelgrass shoot (g).
We analyzed the stability of the equilibria of the
model at varying settings of key parameters. Critical
thresholds were determined by a numerical procedure. The key parameter was increased in small
steps, after which the model was run to stabilize to its
equilibrium. Next, this analysis was also performed
backwards, by decreasing the key parameter in small
steps. These analyses were combined to construct
bifurcation plots of various parameters. We determined unstable equilibria by making the quasi
steady state assumption (dT
dt ¼ 0) and plotting equilibria for different values of the control parameters in
GRIND for MATLAB.
RESULTS
Conceptual Models
Figure 2A and B shows phase planes of the joint
detoxification and growth dilution model, respectively, based on the default settings presented in
Table 1. Both the graphs show two stable equilibria
and one unstable equilibrium (saddle point).
Whereas toxicant concentrations show a straightforward decrease with increasing biomass in the
joint detoxification model, toxicant levels in the
growth dilution model increase again when X nears
its carrying capacity. This is because the population
growth and therefore also the detoxification rate is
highest halfway to the population’s carrying
capacity. Next, we analyzed the sensitivity of both
models to varying values of the maximum toxicant
concentration (Tin) in a one-dimensional bifurcation plot (Figure 2C, D). The results demonstrate
that both models can have alternative stable states,
one without organisms and one with a population
that can alleviate toxicity. The systems collapse to a
bare state when organism density is pushed below
the critical threshold (Figure 2C, D, dashed lines).
A more thorough bifurcation analysis of the joint
detoxification model shows that the conditions for
alternative stable states in this model are relatively
simple. After reducing the number of model
parameters to 2 by non-dimensionalization (online
Appendix 1), conditions for alternative stable state
can be summarized in a simple 2D plot. This plot
shows all parameter combinations at which alternative stable states occur (Figure 3A). It appears
that there are two prerequisites that determine
whether the feedback is strong enough to cause
alternative stable states. First, the equilibrium
concentration of toxicant without organisms (Tin)
should be able to prevent colonization of the
Bistability Through Density-Dependent Toxicity
845
Figure 2. Analyses of the conceptual models. A and B Nullclines at default settings of the ‘‘joint detoxification’’ model
and ‘‘growth dilution’’ model, respectively. The closed dots represent stable equilibria in the models, the open dots are
unstable saddle points. The separatrix indicates the critical boundary above which the population can survive and develop
to the equilibrium. C indicates a colonized state, B is a bare state. C and D Bifurcation analyses of the ‘‘joint detoxification’’
model and ‘‘growth dilution’’ model, respectively, with varying values of Tin. Solid lines represent stable equilibria, whereas
the dashed line indicates unstable equilibria. Dots indicate bifurcation points (F fold bifurcation, T transcritical bifurcation),
arrows show the direction of change. Note that all parameter settings for the ‘‘joint detoxification’’ model and the ‘‘growth
dilution’’ model were identical, except for parameter b, which were set at 0.2 and 1.5, respectively.
organism [that is, its effect on the organisms (b Tin)
should be higher than the maximum growth rate of
the population (a)]. The second prerequisite is that
the effect of a full-grown population (KX) on the
toxic substances should be strong enough to let
the concentration of the toxicant decrease, that is,
the refresh rate of the toxic substance (p) should be
less than the maximum effect of the organisms (KX
d). Note that this means that the chances for alternative equilibria increase if the turnover rate of the
toxic substance (p) is low. If these two prerequisites
are met, there is a range of Tin with alternative
stable states. With increasing carrying capacity (or
decreasing turnover rate), this range increases.
The growth dilution model is too complex for a
similar analytical bifurcation analysis. However, we
did this analysis numerically, showing very similar
results (Figure 3B). Although the range for bistability in this model is narrower when compared to
the joint detoxification model, there is still a rather
large parameter space with alternative stable states.
Moreover, the qualitative effect of scaled toxicity
and carrying capacity is remarkably similar.
Specific Model of NHx Toxicity
in Eelgrass
The eelgrass model was parameterized to describe a
sheltered estuary, where water mixing between the
eelgrass meadow and its surroundings is limited
(Table 2). Water flowing into the seagrass bed has a
NHx concentration of 100 lmol l-1 NHx, a value
comparable to various measurements in the field
(for example, Hauxwell and others 2001; Brun and
others 2002). In these systems pH can vary strongly.
At night, pH is generally around 8 whereas pH can
rise up to 9 or even 10 during the day, due to photosynthesis of algae and seagrass itself (Choo and
others 2002; Feike and others 2007; van der Heide
and others 2008), hence leading to higher NH3
concentrations. For simplicity, we assumed an
average pH of 8.5 for our model system.
846
T. van der Heide and others
Table 1.
Variables and Default Parameter Settings of the Conceptual Model
Default
Variables
X
T
Parameters
a
b
Kx
Tin
p
d1
d2
0.1
0.2–1.5
1
1
1
10
10
Unit
Description
g l-1
mol l-1
Biomass of organism X per liter
Concentration of toxicant T
day-1
l day-1 mol-1
g l-1
mol l-1
day-1
l day-1 g-1
l g-1
Growth rate
Mortality constant; set at 0.2 for model 1 and at 1.5 for model 2
Carrying capacity of X
Maximum concentration of T
Refreshing rate
Uptake constant of T
Uptake constant of T
Note that in this instance, units used in the conceptual model are based upon an organism living in a water body with a constant refreshing rate, for example, (phyto)plankton
or fish.
Figure 3. Two-dimensional plots of the scaled conceptual
models (see online Appendix 1). On the axes are the two
combined parameters: the scaled toxic load a ¼ baTin and
the scaled carrying capacity of X, which is b ¼ dp KX for the
‘‘joint detoxification’’ model and c ¼ dp a K for the ‘‘growth
dilution’’ model. The figures give all parameter combinations where we get alternative stable states. (C colonized,
C/B alternative states, B bare only, F (solid line) fold bifurcation, T (dashed line) transcritical bifurcation).
The nullclines of this model at default parameter
settings are presented in Figure 4A. Similar to the
conceptual model, the graph shows one unstable
equilibrium and two stable points. Depending on
the initial conditions, the meadow will either develop towards carrying capacity or collapse to a
bare state. A bifurcation analysis on the NHx concentration of the water flowing into the eelgrass
meadow (NHxin) reveals that alternative stable
states are present over a wide range of realistic
concentrations, from 75 to over 158 lmol l-1
(Figure 4B). We analyzed the interactive effects of
NHxin, pH, and dilution rate R, because these
parameters are often variable in the field. Results
demonstrate that the effect of the NHx concentration of the incoming water is highly dependent on
both pH and the dilution rate of the water inside
the meadow (Figure 5A, B). The analysis shows
that alternative stable states are present at pH values higher than 7.9 (Figure 5A). Below pH 7.9, the
toxicity of NHx is too low as only little NHx is
present as toxic NH3. Therefore, the meadow tolerates extremely high concentrations of NHx in the
incoming water. Sensitivity to NHx exposure increases strongly with rising pH levels, as the NH4+/
NH3 equilibrium shifts towards NH3. At pH 10,
alternative stable states exist between NHx concentrations of 10 and 55 lmol l-1 in the water
flowing into the meadow. Figure 5B demonstrates
the interactive effects of NHxin and water dilution
rate R. No alternative stable states are present when
the concentration of NHx is below 75 lmol l-1,
because these concentrations are not lethal for the
eelgrass plants at pH 8.5 (compare the first prerequisite of the conceptual model). The effect of
NHx becomes dependent on both NHx input concentrations and the turnover rate R, when NHx
concentrations of the incoming water rise above
Bistability Through Density-Dependent Toxicity
Table 2.
Variables and Default Parameter Settings of the Eelgrass Model
Default
Variables
Z
NHx
NH3
Parameters
r
m
KZ
HNH3
n
pH
ka
NHxin
R
Umax
HNHx
C
DwZ
847
0.0105
0.16
2500
37.432
1.6922
8.5
0.35e-9
100
5
0.492
9.2
0.5
0.44
Unit
Description
sh m-2
mmol m-3 (=lmol l-1)
mmol m-3 (=lmol l-1)
Eelgrass shoot density
Reduced nitrogen concentration
Ammonia concentration
day-1
day-1
sh m-2
mmol m-3 (=lmol l-1)
Maximum net growth rate
Maximum mortality rate
Carrying capacity
Half rate constant for toxic effects of NH3
Hill-curve exponent in NH3 toxicity curve
pH
Dissociation constant for NH3/NH4+
NHx concentration of water coming into the meadow
Dilution rate of the water in the meadow
Maximum uptake rate per g dry weight
Half rate constant for NHx uptake
Canopy height
Dry weight per shoot
mmol m-3 (=lmol l-1)
day-1
mmol g-1 day-1
mmol m-3 (=lmol l-1)
m
g
Source
1
*
2, +
*
*
3, +
4
5
±
6
6
2, +
*
(1) Olesen and Sandjensen (1994), (2) Boström and others (2003), (3) Choo and others (2002) and Feike and others (2007), (4) Khoo and others (1977), (5) Hauxwell and
others (2001) and Brun and others (2002), (6) Thursby and Harlin (1982, (*) recalculated from original data of van der Heide and others (2008), (+) unpublished results, (±)
estimated.
Figure 4. Analyses of the
eelgrass model.
A Nullclines of the model
at default settings.
B Bifurcation analysis of
the model with varying
NHx concentrations in the
incoming water (NHxin).
See Figure 2 for the
meaning of symbols used.
the 75 lmol l-1 threshold. Alternative stable states
exist far beyond NHx concentrations of 500 lmol l-1
for NHxin when R drops below 1 day-1.
DISCUSSION
We show in both a conceptual and a more realistic
model that ‘‘density-dependent toxicity,’’ a positive
feedback mechanism between a population of
organisms and a toxic compound may lead to
bistability in biological systems. Organisms may
alleviate adverse effects of the toxicant by actively
lowering ambient concentrations through either
‘‘joint detoxification’’ or ‘‘growth dilution.’’ Joint
detoxification is a mechanism where the toxicant is
actively broken down by the exposed organisms.
The population can maintain itself, provided that its
biomass is sufficient to reduce toxicant concentrations to a level where organism growth may
equalize or exceed mortality. Growth dilution is a
mechanism where the toxicant is not broken down,
but is stored in the organism’s tissues. Because these
tissues are only able to store a limited amount of
toxicants, they will become saturated. In this case,
reduction of the toxicant is dependent on population growth rather than the biomass present in the
system.
Our eelgrass model suggests that density-dependent
toxicity may indeed be important in real ecosystems.
Although the model is somewhat more complicated,
848
T. van der Heide and others
Figure 5. Two-dimensional bifurcation analyses of the
eelgrass model. A Bifurcation analysis with varying pH
and NHx concentrations in the incoming water (NHxin).
B Bifurcation plot with varying dilution rates of the
water in the meadow (R) and NHx concentrations in the
incoming water (NHxin). Solid lines represent fold bifurcations, whereas the dashed lines indicate transcritical
bifurcations. B indicates a bare state; C/B indicates
the area where alternative stable states occur. Left of the
dashed lines (indicated with C), eelgrass presence is the
only stable state.
its essence is identical to our conceptual joint detoxification model. Sudden die-off events caused by high
reduced nitrogen (NHx) loads, combined with a high
pH may be prevented by joint uptake if shoot density of
the meadow is high enough. This mechanism fails if
shoot densities are pushed below a certain threshold,
resulting in a shift to a bare state. This illustrates
that density-dependent toxicity can have important
implications for toxicity research and management in
ecosystems. For toxicity research in laboratory and
field studies, our results indicate that it may be very
important to choose realistic population densities instead of working with standardized biomass or densities. Moreover, our simulations also show that it is not
sufficient to measure ambient toxicant levels to
assess ecosystem health. At high population densities,
toxicant levels may be low due to detoxification
mechanism, whereas the toxicant load may actually be
very high. Therefore, ecosystem monitoring should
focus on determining the toxicant load in such cases.
Finally, it should also be noted that when such an
ecosystem collapses, it may not only affect the community structure directly. After the collapse many
associated species may now also experience toxicity
effects because toxicant levels will increase dramatically.
Although we studied only one example, densitydependent toxicity is most likely an important
mechanism in a wide range of biological systems.
Joint detoxification has also been reported in for
example isoetid macrophytes. In these vegetations,
ammonium toxicity can be prevented because
ammonium concentrations in the pore water are
actively lowered, not only by uptake, but also by
density-dependent oxidation of ammonium to
nitrate due to high radial oxygen loss of the roots
(Smolders and others 2002). Toxic effects of sulfide
in salt-marshes (Webb and others 1995; Webb and
Mendelssohn 1996), seagrasses (for example,
Goodman and others 1995; Pedersen and others
2004) or sulfate-rich freshwater wetlands (Lamers
and others 1998; Armstrong and Armstrong 2001;
van der Welle and others 2006) may be prevented
in a similar way. In these systems, sulphide can be
oxidized to harmless sulfate if oxygen loss by the
root system is sufficiently high.
A second possible mechanism for densitydependent toxicity, growth dilution, may for
instance reduce toxic effects of heavy metals; toxicants that cannot be broken down. The dilution
effect increases tolerance of microbes to heavy
metal exposure (Duxbury and McIntyre 1989). In
aquatic ecosystems, accumulation of toxic metals in
the trophic chain of food webs has been shown to
be reduced with increasing concentrations of phytoplankton (Pickhardt and others 2002) or even
with increasing nutritional quality of the algae
(stoichiometric dilution) (Karimi and others 2007).
Although our analyses suggest that the mechanism presented in this study may lead to alternative
stable states in many biological systems, it should be
noted that dynamics in our models are described in
a simplified manner. This implies that the models
may disregard or oversimplify processes that might
in reality be important. These can include factors
that weaken the positive feedback as well as processes that enhance it. In general, processes
strengthening the feedback may include symbiosis
or natural selection leading to more resistant individuals (Brook 1989), whereas factors weakening it
can include limitation of resources (for example,
Bistability Through Density-Dependent Toxicity
nutrients, water) (Weidenhamer 1996), competition with other species (Weidenhamer 1996), or
disease (van der Heide and others 2007). More
specifically, a factor that could weaken the positive
feedback in our eelgrass model is that high shoot
densities may imply a higher photosynthetic activity, leading to a higher pH in conditions with low
flow rates and poor mixing. High pH in turn may
lead to increased ammonia toxicity (van der Heide
and others 2008). Additionally, low flow rates may
result in temporary spikes in ambient NHx concentrations at the end of the growing season due to
natural die-off of eelgrass itself. In contrast to systems with higher flow rates, export of seagrass litter
in sheltered embayments may be slow. This may
cause decomposing litter to temporarily accumulate
in the system, resulting in increased release of NHx.
Still, despite the fact that the described mechanism
might not lead to hysteresis in all biological systems,
either due to interfering factors or simply because
the feedback mechanism is too weak, densitydependent toxicity may still be important. In such
systems, feedbacks may still cause a strong nonlinear response of organism density to changing toxicant loads (for example, a sharp sigmoid response),
leading to unexpectedly sudden community shifts
and ecosystem management problems (Scheffer
and others 2001).
In summary, we present a feedback mechanism
between organisms and toxic compounds that may
potentially lead to bistability in biological systems.
Adverse effects of toxicants that are being produced
in or come into the system may be prevented by
actively lowering ambient concentrations through
either rapid joint detoxification or growth dilution.
The presented general mechanism may be important in a wide range of biological systems.
ACKNOWLEDGEMENTS
We wish to thank the editor and two anonymous
referees for their valuable comments on earlier
versions of the manuscript. This study was financially supported by the Netherlands Organization of
Scientific Research/Earth and Life Sciences (NWOALW).
OPEN ACCESS
This article is distributed under the terms of the
Creative Commons Attribution Noncommercial
License which permits any noncommercial use,
distribution, and reproduction in any medium,
provided the original author(s) and source are
credited.
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